Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.     

A diagnostic for Cox regression with discrete failure-time models

Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete-one statistics can be approximated analytically from a one-step Newton-Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one-step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure-time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.     

Survival analysis in clinical trials: past developments and future directions

The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments in this field that have had the most profound impact on clinical trials are the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) method for estimating the survival function, the log-rank statistic (Mantel, 1966, Cancer Chemotherapy Report 50, 163-170) for comparing two survival distributions, and the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting-process martingale theory pioneered by Aalen (1975, Statistical inference for a family of counting processes, Ph.D. dissertation, University of California, Berkeley) provides a unified framework for studying the small- and large-sample properties of survival analysis statistics. Significant progress has been achieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interval-censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysian methods.     

A Most Probable Number method (MPN) for the estimation of cell numbers of heterotrophic nitrifying bacteria in soil

A Most Probable Number (MPN) method was developed allowing for the first time estimation of populations of bacteria capable of heterotrophic nitrification. The method was applied to an acidic soil of a coniferous forest exhibiting nitrate production. In this soil nitrate production was unlikely to be catalyzed by autotrophic nitrifiers, since autotrophic ammonia oxidizers never could be detected, and autotrophic nitrite oxidizers were usually not found in appreciable cell numbers. The developed MPN method is based on the demonstration of the presence/absence of nitrite/nitrate produced by heterotrophic nitrifying bacteria during growth in a complex medium (peptone-meat-extract softagar medium) containing low concentrations of agar (0.1%). Both the supply of the growing cultures in MPN test tubes with sufficient oxygen and the presence of low agar concentrations in the medium were found to be favourable for sustainable nitrite/nitrate production. The results demonstrate that in the acidic forest soil the microbial population capable of heterotrophic nitrifcation represents a significant part of the total aerobic heterotrophic population. By applying the developed MPN method, several bacterial strains of different genera not previously described to perform heterotrophic nitrification have been isolated from the soil and have been identified by bacterio-diagnostic tests.     

Nitrogen Cycling and Nitric Oxide Emissions in Oil-Impacted Prairie Soils

A remote site in the Tallgrass Prairie Preserve of Oklahoma (The Nature Conservancy) was contaminated with crude oil from a pipeline break and is being bioremediated using landfarming techniques. Landfarming is designed to stimulate microbial-based catabolism of petroleum through combined dilution/mixing and fertilization-based effects. To evaluate nitrogen-based effects during remediation, the site was sectioned and treated with urea, ammonium sulfate, or ammonium nitrate. Samples were obtained from prairie soil without chemical nitrogen addition and with or without hydrocarbon contamination. Nitrogen cycling dynamics were followed by measuring ammonium, nitrite, nitrate, and volatile nitric oxide (NO_x) levels. Nitrifying and denitrifying bacterial numbers were estimated and compared to soil oxygen, carbon dioxide, and methane levels as well as to overall total petroleum hydrocarbon (TPH) reduction. For a prairie ecosystem of this type, a high level of fertilization, particularly with nitrogen, can have ecological effects almost as profound as the petroleum contamination itself. Fertilization of the oil-contaminated soil with the reduced and/or oxidized forms of nitrogen quickly resulted in elevated steady-state levels of both ammonium and nitrate, and exceptionally high levels of NO_x released from soil. Although nitrogen fertilization increased microbial nitrogen metabolism and nitrogen cycling, it had minimal effects on the overall remediation efficiency.     

Epidemics with partial immunity to reinfection

We obtain analytical results about epidemics generated by the partial immunity model of Gomes et al. [3], in which infection confers partial immunity to reinfection. When the demographic process is excluded, the behavior switches from epidemic to endemic as the basic reproduction number R₀ crosses the reinfection threshold . We derive formulas for two quantities characterizing the size of the epidemic below the reinfection threshold: the attack rate A, which is the fraction of the population infected at least once, and the final size Z, which is the average number of infections per individual. We also derive a system of differential equations which can be used to obtain more detailed information, such as the fraction of the population infected n times throughout the epidemic, for every n.     

Evaluation of effectiveness of enhanced‐efficiency fertilizers as mitigation options for N2O and NO emissions from agricultural soils: meta‐analysis

Agricultural fields are an important anthropogenic source of atmospheric nitrous oxide (N₂O) and nitric oxide (NO). Although many field studies have tested the effectiveness of possible mitigation options on N₂O and NO emissions, the effectiveness of each option varies across sites due to environmental factors and field management. To combine these results and evaluate the overall effectiveness of enhanced‐efficiency fertilizers [i.e., nitrification inhibitors (NIs), polymer‐coated fertilizers (PCFs), and urease inhibitors (UIs)] on N₂O and NO emissions, we performed a meta‐analysis using field experiment data (113 datasets from 35 studies) published in peer‐reviewed journals through 2008. The results indicated that NIs significantly reduced N₂O emissions (mean: ?38%, 95% confidential interval: ?44% to ?31%) compared with those of conventional fertilizers. PCFs also significantly reduced N₂O emissions (?35%, ?58% to ?14%), whereas UIs were not effective in reducing N₂O. NIs and PCFs also significantly reduced NO (?46%, ?65% to ?35%; ?40%, ?76% to ?10%, respectively). The effectiveness of NIs was relatively consistent across the various types of inhibitors and land uses. However, the effect of PCFs showed contrasting results across soil and land‐use type: they were significantly effective for imperfectly drained Gleysol grassland (?77%, ?88% to ?58%), but were ineffective for well‐drained Andosol upland fields. Because available data for PCFs were dominated by certain regions and soil types, additional data are needed to evaluate their effectiveness more reliably. NIs were effective in reducing N₂O emission from both chemical and organic fertilizers. Moreover, the consistent effect of NIs indicates that they are potent mitigation options for N₂O and NO emissions.     

Interaction among Non-toxic Phytoplankton,Toxic Phytoplankton and Zooplankton: Inferences from Field Observations

We explore the mutual dependencies and interactions among different groups of species of the plankton population, based on an analysis of the long-term field observations carried out by our group in the North–West coast of the Bay of Bengal. The plankton community is structured into three groups of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. To find the pair-wise dependencies among the three groups of plankton, Pearson and partial correlation coefficients are calculated. To explore the simultaneous interaction among all the three groups, a time series analysis is performed. Following an Expectation Maximization (E-M) algorithm, those data points which are missing due to irregularities in sampling are estimated, and with the completed data set a Vector Auto-Regressive (VAR) model is analyzed. The overall analysis demonstrates that toxin-producing phytoplankton play two distinct roles: the inhibition on consumption of toxic substances reduces the abundance of zooplankton, and the toxic materials released by TPP significantly compensate for the competitive disadvantages among phytoplankton species. Our study suggests that the presence of TPP might be a possible cause for the generation of a complex interaction among the large number of phytoplankton and zooplankton species that might be responsible for the prolonged coexistence of the plankton species in a fluctuating biomass.     

Convergent Evolution of Human and Bovine Haptoglobin: Partial Duplication of the Genes

Haptoglobin (Hp) is a hemoglobin-binding plasma protein consisting of two types of chains, called α and β, which originate from a common polypeptide. In humans, but not in other mammals, Hp has been shown to occur in two allelic forms, Hp1 and Hp2, which differ in the length of the α-chain. The longer α-chain (in Hp2) seems to have arisen by an internal duplication of a gene segment coding for almost the entire α-chain of Hp1. In this article we show that Hp of cow (Bos taurus) contains an α-chain, the structure of which is similar to that of the human Hp2 α-chain. Furthermore, comparison of the structure of bovine Hp and human Hp2 suggests that the bovine gene arose by a duplication of the gene segment homologous to that duplicated in human Hp2. However, a phylogenetic analysis indicates that the two genes were formed independently. The evolutionary pressure that has led to the fixation of the Hps with a longer α-chain is not known. Reviewing Editor: Dr. Manyuan Long